 Moving between Abel's and Schroeder's Functional Equations - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Moving between Abel's and Schroeder's Functional Equations (/showthread.php?tid=1251) Moving between Abel's and Schroeder's Functional Equations - Daniel - 01/07/2020 Check out Moving between Abel's and Schroeder's Functional Equations RE: Moving between Abel's and Schroeder's Functional Equations - sheldonison - 01/16/2020 (01/07/2020, 03:55 PM)Daniel Wrote: Check out Moving between Abel's and Schroeder's Functional Equations Hey Daniel, what if Then Schroeder's equation , but is complex.   Personally I think I prefer instead of for the complex valued Abel function. There is a pair of complex valued Abel functions for the two complex conjugate fixed points, and there is a singularity at Anyway, Kneser's tetration uses a Riemann mapping of , wrapping the real axis around a unit circle to eventually get to  where there are two 1-cyclic theta(z) functions   where k is a constant as Im(z) gets arbitrarily large, and Kneser's slog or the inverse of Tetration would be tau^{-1}(z) is also a z+1-cyclic function used to generate Tet(z) from the inverse of the complex valued Abel function. https://math.eretrandre.org/tetrationforum/showthread.php?tid=213 https://math.stackexchange.com/questions/2308409/operational-details-implementation-of-knesers-method-of-fractional-iteration/2308955#2308955